Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 2001, 2009 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 2001 and 2009 is 1.
GCF(2001,2009) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 2001
3 | 2001 |
23 | 667 |
29 | 29 |
1 |
Prime factors of 2001 are 3,23,29. Prime factorization of 2001 in exponential form is:
2001 = 31×231×291
Prime Factorization of 2009
7 | 2009 |
7 | 287 |
41 | 41 |
1 |
Prime factors of 2009 are 7,41. Prime factorization of 2009 in exponential form is:
2009 = 72×411
∴ So by taking common prime factors GCF of 2001 and 2009 is 1
Factors of 2001
List of positive integer factors of 2001 that divides 2001 without a remainder.
1,3,23,29,69,87,667,2001
Factors of 2009
List of positive integer factors of 2009 that divides 2009 without a remainder.
1,7,41,49,287,2009
Greatest Common Factor
We found the factors and prime factorization of 2001 and 2009. The biggest common factor number is the GCF number.
So the greatest common factor 2001 and 2009 is 1.
Also check out the Least Common Multiple of 2001 and 2009
(i) The GCF of 2001 and 2009 is associative
GCF of 2001 and 2009 = GCF of 2009 and 2001
1. What is the GCF of 2001 and 2009?
Answer: GCF of 2001 and 2009 is 1.
2. What are the Factors of 2001?
Answer: Factors of 2001 are 1, 3, 23, 29, 69, 87, 667, 2001. There are 8 integers that are factors of 2001. The greatest factor of 2001 is 2001.
3. What are the Factors of 2009?
Answer: Factors of 2009 are 1, 7, 41, 49, 287, 2009. There are 6 integers that are factors of 2009. The greatest factor of 2009 is 2009.
4. How to Find the GCF of 2001 and 2009?
Answer:
Greatest Common Factor of 2001 and 2009 = 1
Step 1: Find the prime factorization of 2001
2001 = 3 x 23 x 29
Step 2: Find the prime factorization of 2009
2009 = 7 x 7 x 41
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = = 1
Step 4: Therefore, the greatest common factor of 2001 and 2009 is 1